In a previous paper, we developed a model to estimate the terminal bulk modulus of sandstones using their petrographic and petrophysic description. The above mentioned model is summarized. A method which is introduced in the previous formulation is then developed to estimate the evolution of the bulk modulus as a function of confining pressure. The role played by the cement and the cracks is emphasized. We test the model using a basic data set in which the bulk moduli have been measured for 17 different sandstones for confining pressures up to 100 MPa.